Training Teachers in the Effective Mathematical and Pedagogical Uses of Software

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Training Teachers in the EffectiveMathematical
and PedagogicalUses of Software
Perspectives from the Dynamic Number and Dynamic
Geometry in Classrooms Projects
Zhonghong Jiang, Texas State University, San
Marcos Daniel Scher, KCP Technologies Scott
Steketee, KCP Technologies
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The Dynamic Number Project

• Builds on the paradigm of Dynamic Geometry
• Dynamic Number The direct manipulation of number
  representations and numerical constructions
• Goal The development of software tools to deepen
  students' conceptions of integers, fractions,
  decimals, real numbers, and early algebra in
  grades 28 mathematics

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The Dynamic Geometry in Classrooms Project

• Randomized controlled trial of an approach to
  high-school geometry that utilizes Dynamic
  Geometry software and supporting instructional
  materials to supplement ordinary instructional
  practices.
• Goal Test the hypothesis that the use of Dynamic
  Geometry software to engage students in
  constructing mathematical ideas through
  experimentation, observation, data recording,
  conjecturing, and proof results in better
  geometry learning for most students.

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The Dynamic Number Project
The Dynamic Geometry in Classrooms Project
curriculum software innovation
randomized controlled trial
professional development
76 classrooms
field testing
students experiment...
number lines
teachers develop technical skills
...observe...
dynamic number grids
...conjecture...
teachers improve instructional strategies
geometric functions
...and prove.
fraction representations
do students learn geometry better?
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Shared Aspects of Our Two Projects

• The Geometers Sketchpad
• A belief that technology, when properly used, can
  foster mathematical growth in both teachers and
  students
• The need for professional development so that
  teachers can learn the technology and use it well
  to promote the goals of the project

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Goals of Technology-Centered PD
Low-End Goals
Participants learn the nuts and bolts of the
software Participants see how the software can
help them accomplish exactly what they already do
when teaching mathematics
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Goals of Technology-Centered PD
High-End Mathematical Goals

• Make the mathematics primary Teachers learn the
  software in the context of exploring meaningful
  mathematics. How the software works is viewed as
  secondary to what it allows them do.

• Deepen teachers mathematical understanding
  Teachers gain a deeper understanding of the
  mathematics they already know and even learn
  some new mathematics as a result of using the
  software.

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Goals of Technology-Centered PD
High-End Pedagogical Goals
Teachers emphasize high-order thinking. Teachers
consider how use of the software can engage
students in higher-order thinking than was
possible without the software.
Teachers modify instructional strategies. Teachers
observe, consider, and adopt new strategies
known to be appropriate to and effective with the
technology.
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Professional Development Issues

• Teacher satisfaction with PD is often low. I
  have a colleague who calls professional
  development drive-by trainings its a good way
  of describing what we get.
• PD is often ineffective. For instance, the recent
  Middle School Mathematics Professional
  Development Impact Study showed very little
  change in teacher behavior, even for a putatively
  well-designed PD intervention.

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Todays Session

• Provide an overview of the professional
  development aspects of our respective projects.
• Consider how to conduct technology PD to maximize
  teacher satisfaction and classroom effectiveness.
• Engage you in thinking and sharing your thoughts
  on how PD that focuses on technology can set its
  sights on the high-end mathematical and
  pedagogical goals weve described.

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The Dynamic Number Project
The field test population
Five elementary schools and one middle school in
New York, Pennsylvania, Georgia, and California
18 teachers
Role of the teachers

• Field test and critique new Sketchpad activities

Collaborate with us to develop Sketchpad
activities
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Goals of the Online Course

• Provide an intensive introduction to Sketchpad
• Focus on elementary number and early algebra
  concepts, but not to the exclusion of geometry
• Promote discussions of the barriers to
  introducing technology and ways to overcome them
• Ask teachers to reflect on the pedagogical and
  mathematical implications of using Sketchpad
• Develop teachers' confidence in breaking out of a
  lockstep approach to implementing Sketchpad-based
  activities

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Six weeks in length
Grades based on projects and participation
Details of the Course
Two moderators Scott and Daniel
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The Dynamic Geometry in Classrooms Project

• The professional development component of this
  project, for project years 1 and 2, consists of a
  summer institute (5 full-day sessions) and the
  academic year follow-up (6 Saturday half-day
  sessions).
• An approach of integrating technology,
  mathematics, and pedagogy in the professional
  development training
• A support system needed to help the participating
  teachers in applying what they have learned from
  the PD into their classrooms

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Teachers Learn Software in the Context of
Exploring Meaningful Mathematics

• The nature of the PD sessions is interactive and
  emphasizing participants active involvement and
  the conceptual understanding of mathematics.
• Important mathematics concepts, processes, and
  relationships are presented or revisited through
  conjecturing-investigating-proving tasks, usually
  challenging problem situations.
• These tasks/situations are explored with the
  dynamic geometry (DG) software as a tool.
  Teachers learn DG skills in the process of using
  them to tackle the tasks/problems.
• Through their learning experiences, teachers
  clearly see how DG environment encourages and
  facilitates mathematical investigations.
• The sessions were designed to accommodate some
  participants who were novice users and others who
  were more experienced.

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Teachers Explore the Pedagogy Needed To Use the
Software Well in Their Classrooms

• The participant-centered, inquiry-based training
  method models the instructional ideas and
  strategies wed like teachers to use.
• To further help teachers to consider changes in
  their instructional strategies, in the relation
  between them and their students, and in how they
  facilitate student learning, mathematical
  explorations are always followed by discussions
  on questions such as How will you teach this
  content in your classrooms using DG software?
  and How will you lead your students in
  conjecturing and proving using DG software?
• All participants in groups of 3 or 4 prepare
  lesson plans to present to the entire group.

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Classroom Observations for Selected Teachers

• The project staff members visit the participating
  teachers classrooms regularly to monitor the
  implementation of the DG treatment, get to know
  whether the teachers need help, and are able to
  provide timely assistance.
• Eighteen teachers were randomly selected through
  stratified sampling (stratified at the number of
  years teaching geometry and the types of classes
  they are teaching).
• Each of the selected teachers is observed five
  times. The five observations are evenly
  distributed throughout the entire school year.
• The observers use the Classroom Observation
  Protocol that the project has developed to score
  each class observed or to be observed.

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The power of the DG approach itself
Graduate credit (3) for successful completion of
the professional development
Stipends
Incentives
Instructional materials from Key Curriculum Press
Personal copy of the Geometers Sketchpad
software
The GSP software for the school computer lab(s)
G. Travel funds for selected teachers to attend
state mathematics conferences and make group
presentations
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Campus Level Team Work

• Organize learning communities among teachers at
  the same school or conveniently nearby schools.
• Teachers cooperate with each other by offering
  and requesting help and deal collaboratively with
  instructional/learning issues that result as part
  of the DG implementation.
• Each team has a leader and he/she interacts with
  the project staff members frequently.

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An On-line Help Component
The project uses the university TRACS system to
include an on-line Help component to provide
teachers with on-going support by sharing success
stories, giving DG instructional suggestions that
are frequently updated, providing links to
various DG resources, etc.
Specifically the Key Curriculum Press is very
supportive, and provides each DG group teacher
with free access to Key Online Sketchpad
LessonLink which contains hundreds of Dynamic
Mathematics activities aligned to the textbooks
and state standards.
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Build Stronger Collaborative Relationships with
School Districts

• The project research team makes great efforts to
  build stronger collaborative relationships with
  the participating school districts so that the
  school/district administration is always
  supportive for the participating teachers to both
  continue their own professional development
  effort and implement the DG approach in their
  classrooms.
• Examples of such efforts include constant
  discussions with school/district
  administrators/masters teachers on important
  issues such as how to encourage teachers' active
  participation and avoid attrition, and
  collaborative presentations at professional
  meetings.